1. Field of the Invention
This invention is categorized as an educational aid for students of mathematics, The construction and operation of this teaching aid can help elementary and middle grade students understand equations involving addition, subtraction, multiplication, division, and multiple as well as single degree unknowns.
2. Description and Relationship of Prior Art
U.S. Pat. No. 3,788,541 also covers a mechanical computer. However the goal of U.S. Pat. No. 3,788,541 is to provide accuracies similar to those achieved by a very large slide rule. By utilizing reels of tape, instead of rule length, U.S. Pat. No. 3,788,541's approach remains compact in size. The goals, construction, and utilization of the computer as described in this application are completely different from referenced U.S. Pat. No. 3,788,541.
U.S. Pat. Nos. 3,949,491, 3,928,923, 4,106,220, 4,713,009, 4,731,022, and European Patent EP - 240-574-A, and British Patent 1,407,899, all involve single balancing beam teaching aid apparatus to help young students with solutions to equations involving only single degree unknowns, such as 2+X=7; 3N=18; 2X+(-X)+3=2(-X)+15; and 27/3=R. U.S. Pat. No. 3,000,114 involves multiple balancing beams, but with no facility for changing a lever arm length on either side of any beam. It follows that U.S. Pat. No. 3,000,114 does not indicate the ability to solve any multiple degree equations.
Equations having multiple degree unknowns have very important and widespread use throughout science and industry, Examples are included later that involve:
(a) a 4th degree equation for finding the radius of a rod having a given twisting torque T, shear modulus E, and length L--as used extensively in the automotive industry; PA1 (b) a 3rd degree equation for finding the radius of a sphere--a soft ball--when knowing the ball's volume; PA1 (c) a 2nd degree equation for finding the direct current in an automobile light bulb when knowing its resistance and its wattage rating. PA1 (a) a mechanical, analog type, teaching aid computer--free of any required electrical, or mechanical spring, power source; PA1 (b) a computer that requires a sense of manipulative touch, as well as a sense of balance--motor nerve inputs to student's brain that bolster understanding and memory; PA1 (c) a computer that allows solutions to multiple degree, as well as single degree, equations; PA1 (d) a computer that allows a student to use one or more sliding weights, and/or placable torques or forces provided by one or more adjacent moving axis beams, to achieve solution to equations involving addition, subtraction, division, and single and multiple degree unknowns; PA1 (e) a computer with more than two connectable beams and with multiple weight channels, that may be needed accomplishing solutions to addition and subtraction problems involving many numbers--by locking connected moveable beam mounting strips in positions so that all beam weight channels can be used; PA1 (f) a computer that allows a student to observe a range of non-answers, as well as one or more answers, to single and multiple degree equations; PA1 (g) a computer whose workability can be easily seen and understood. The basic concept of balancing torques is gained by a child early on. A heavy child automatically sits closer to the fulcrum of a teeter-toter to offset the torque of a lighter child that sits further back from the fulcrum. Thus, a student may be attracted to the use of this teaching aid because of his or her confidence in understanding the computer's basic functions. PA1 (h) a computer composed of a group of interconnecting balancing beams that only requires understandable settings and manipulative balancing. Such activity should challenge and intrigue young students with their sense of accomplishment having an ability to solve otherwise too-complex problems--the type of multiple degree problems that are involved with equations similar to ones that one of their relatives or acquaintances may utilize at work. Thus, the young student may be viewed by elders with astonishment and accompaning praise. What better motivation would there be to encourage our country's hoped for, forthcoming generation of scientists and engineers.
A separate list includes some common multiple degree equations.
Studies have shown that young students are capable of learning concepts involved with equations having multiple degree unknows. However, there is no manipulating type of mechanical computer teaching aid that will help in understanding and solving a multiple degree equation such as -2X.sup.4 -5X.sup.3 +10X.sup.2 -4X+16=0. Later in this application, an example of the simple set up and solution of such a 4th degree equation is illustrated. This invention's teaching aid will reinforce the students' understanding and memory of the equation solution process, in addition to discovering problem solutions.
Since all of the referenced patents involve only a single balance beam, it will be revealed by a comparison to representative patent '491, FIGS. 4, 6, and 8, versus this application's FIGS. 1 and 2, that in order for '491 to arrive at a total weight, shown as 44, at a specific beam lever arm, shown as -6 in FIG. 6, or -8 in FIG. 8, several component weights must first be added mentally, then stacked correctly, before a desired confirmation, as in FIG. 8, that 8.times.3=24. With this application's approach, by comparison, it is easier, faster, and has less likelihood of error, to slide a 1 unit weight to a +4 position on a second beam, than to stack four 1 unit weights at a number 1 position on a single beam.
The stacking of weights, involved with the referenced patents' single beams, could raise the grouped weights' center of gravity too high for a proper, narrow band, accurate, beam balancing movement.
All of the referenced patents are limited in that whenever their single beam is used for solutions to multiplication or division problems, at least one stacked weight, or substitution weight is required, along with its disadvantages.
Only this application's multiple interconnecting beam approach overcomes the stated disadvantages or limitations with stacking or substituting weights: (a) increased required time; (b), higher weight center of gravity, and (c), likelihood of error.
Further, here, by using a group of interconnecting balancing beams, with each beam having at least a 1 unit and 10 unit weight, along with decimal marked positions for settings; the decimal system can be taught and used,
A large part of a student's attraction to, and confidence in, a teaching aid computer stems from an understanding of how it works, Today's popular teaching aid computers have complex electronic circuitry that is seldom understood by the user. Therefore, the student most often must proceed on blind faith the computer's capability. If an error occurs, the student can only check his programming, not the way that program is processed through the computer's circuitry. This application's teaching aid computer has exposed workability that is easily understood and therefore bolsters confidence and attraction in its use.
Later, FIGS. 3 through 7, are directed to an understanding of the computer's workability as well as its use in problem solution.